一类离散相依索赔风险模型的随机分红问题

数学物理学报 ›› 2022, Vol. 42 ›› Issue (2): 631-640.

• 论文 • 上一篇

一类离散相依索赔风险模型的随机分红问题

陈密^1,^2,³,聂昌伟¹,刘海燕^1,^2,*()

¹ 福建师范大学数学与统计学院福州 350117
² 福建省分析数学及应用重点实验室福州 350117
³ 福建省应用数学中心(福建师范大学) 福州 350117

收稿日期:2020-11-17 出版日期:2022-04-26 发布日期:2022-04-18
通讯作者: 刘海燕 E-mail:rain6397@163.com
基金资助:
国家自然科学基金(11701087);国家自然科学基金(11701088);福建省自然科学基金(2018J05003);福建省自然科学基金(2019J01673);福建省高校创新团队培育计划和福建师范大学校创新团队"概率与统计: 理论和应用"(IRTL1704)

Randomized Dividends in a Discrete Risk Model with Time-Correlated Claims

Mi Chen^1,^2,³,Changwei Nie¹,Haiyan Liu^1,^2,*()

¹ School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117
² Fujian Provincial Key Laboratory of Mathematical Analysis and its Applications, Fuzhou 350117
³ Center for Applied Mathematics of Fujian Province (Fujian Normal University), Fuzhou 350117

Received:2020-11-17 Online:2022-04-26 Published:2022-04-18
Contact: Haiyan Liu E-mail:rain6397@163.com
Supported by:
the NSFC(11701087);the NSFC(11701088);the NSF of Fujian Province(2018J05003);the NSF of Fujian Province(2019J01673);the Program for Innovative Research Team in Science and Technology in Fujian Province University and "Probability and Statistics: Theory and Application" of Fujian Normal University(IRTL1704)

摘要/Abstract

摘要：

该文将随机保费收入、相依索赔以及随机分红策略引入到复合二项风险模型中, 并研究该模型下的随机分红问题. 运用母函数的方法, 推导得到保险公司直至破产前的期望累积折现分红量满足的差分方程及其解. 最后, 通过几个数值例子展示了所得结果.

关键词: 期望累积折现分红量, 相依索赔, 随机保费收入, 随机分红策略

Abstract:

In this paper, the compound binomial risk model is extended by involving the random premium income with time-correlated claims and random dividend strategy. By the method of generating function, the difference equation and its solution for the expected cumulated discounted dividends until ruin are obtained. Finally, the effect of related parameters on the total expected discounted dividends are shown in several numerical examples.

Key words: The expected cumulated discounted dividends, Time-correlated claims, Stochastic premium income, Randomized dividend policy

中图分类号:

O211.6

陈密,聂昌伟,刘海燕. 一类离散相依索赔风险模型的随机分红问题[J]. 数学物理学报, 2022, 42(2): 631-640.

Mi Chen,Changwei Nie,Haiyan Liu. Randomized Dividends in a Discrete Risk Model with Time-Correlated Claims[J]. Acta mathematica scientia,Series A, 2022, 42(2): 631-640.

图/表 3

表 1

表 2

表 3

参考文献 26

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$V(u, b)$	$u=0$	$u=1$	$u=2$	$u=3$	$u=4$	$u=5$	$u=6$	$u=7$	$u=8$
$v=0.96$	1.3615	1.6118	1.8653	2.0968	2.1991	2.2684	2.3146	2.3449	2.3649
$v=0.93$	0.6677	0.8219	0.9908	1.1639	1.2221	1.2614	1.2873	1.3041	1.3150
$v=0.90$	0.3999	0.5123	0.6439	0.7910	0.8309	0.8579	0.8579	0.8873	0.8950

$V(u, b)$	$u=0$	$u=1$	$u=2$	$u=3$	$u=4$	$u=5$	$u=6$	$u=7$	$u=8$
$\theta=0$	0.7612	0.9249	1.0882	1.2519	1.4327	1.6373	1.8703	2.1362	2.4399
$\theta=0.25$	0.7121	0.8950	1.0591	1.2205	1.3975	1.5972	1.8246	2.0840	2.3803
$\theta=0.5$	0.6689	0.8687	1.0336	1.1930	1.3665	1.5620	1.7845	2.0382	2.3279
$\theta=0.75$	0.6307	0.8454	1.0109	1.1686	1.3391	1.5309	1.7489	1.9976	2.2816
$\theta=1$	0.5966	0.8246	0.9908	1.1468	1.3147	1.5031	1.7172	1.9614	2.2403

$V(u, b)$	$b=1$	$b=2$	$b=3$	$b=4$	$b=5$	$b=6$	$b=7$	$b=8$	$b=9$	$b=10$
$u=1$	1.6893	1.4971	1.3001	1.1123	0.9449	0.8003	0.6765	0.5710	0.4816	0.4058
$u=2$	1.9841	1.9125	1.6609	1.4209	1.2072	1.0223	0.8642	0.7296	0.6153	0.5184
$u=3$	2.2042	2.1461	2.0305	1.7371	1.4759	1.2499	1.0565	0.8919	0.7522	0.6338
$u=4$	2.3646	2.3201	2.2204	2.0786	1.7660	1.4955	1.2641	1.0672	0.9001	0.7584
$u=5$	2.4837	2.4489	2.3625	2.2405	2.0902	1.7701	1.4963	1.2632	1.0654	0.8976

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一类离散相依索赔风险模型的随机分红问题

Randomized Dividends in a Discrete Risk Model with Time-Correlated Claims

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